Control Systems and Computers, N2, 2019, Article 2

Upr. sist. maš., 2019, Issue 2 (280), pp. 16-24.

UDC 004.94

V.Yu. KOROLYOV, PhD (Eng.), Senior Research Associate,
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, 40, Acad. Glushkova Ave., 03187, Kyiv, Ukraine, E-mail:


Introduction. Missile weapons have complex logistics, there is low-volume product with high cost. The testing of a number of Ukrainian missiles of various uses raises the question of improving the efficiency of their use. Therefore, the actual scientific task is to increase the effectiveness of its application and to ensure reuse whenever possible.

Purpose. The purpose of the article is to optimize the routing of multiple-use cruise missiles (MUCMs) provided that the enemy is countered.

Methods. For a meaningful statement of the optimization problem, a probabilistic model of rocket firing was considered, taking into account counteraction of the enemy, decomposition of tasks, hierarchical construction of the models of combat actions for MUCMs, probability theory, combinatorial optimization.

Result. A meaningful statement of the problem of combinatorial optimization for the swarm of MUCMs is executed. It is shown that this problem can be considered as a routing task for vehicle with random data (Stochastic VRP, SVRP). The consideration is given to the estimation of the required amount of MUCMs and the methods of solving the problem are proposed.

Conclusion. For the first time, a meaningful statement of the routing problem for a swarm of MUCMs, which is anupcoming weapon, is proposed. It is shown that the mathematical model of the motion of MUCMs can be reduced to the model of routing of vehicles with several depots. The hierarchy of models for research operations of attack on the object by a swarm of cruise missiles and constructed decomposition of tasks has been given, which allows us to continue research in this direction in order to maximize economic efficiency use of missiles.

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Keywords: routing problem, combinatorial optimization, model of vehicles with multiple depots, cruise missile.

  1. Gorbulin, V.P., Gulianitsky, L.F., Sergienko, I.V., 2019. “Statements and mathematical models of problems of optimization of routes of aircraft with dynamic depots”. Upravlâûŝie sistemy i mašiny, 1, pp. 3–10. (In Ukrainian).
  2. Golden, B., Raghavan, S., Wasil, E., 2008. The Vehicle Routing Problem: Latest Advances and New Challenges, New York: Springer-Verlag US, 591 p,
  3. Gulianitsky, L.F., 2007. “Problem of optimization of routes of vehicles with time windows”. Computer mathematics, 1, pp. 122–132. (In Ukrainian).
  4. Korolyov, V.Yu., Ogurtsov, M.I., 2017. “Transport and communication problem for groups of unmanned vehicles”. Mathematical Machines and Systems, 1, pp. 82–89. (In Ukrainian).
  5. Ogurtsov. M.I., Hodzinsky. O.M.. 2016. “Development of algorithms for solving the problem of routing vehicles with time windows”. Computer mathematics, 1, pp. 134–142. (In Ukrainian).
  6. Korolyov, V.Yu., Hodzinsky, O.M., 2018. “Topology-Combinatoric Model for Building Networks of Vehicles”. Computer Mathematics, 1, pp. 61–67. (In Ukrainian).
  7. Korolyov, V.Yu., Polinovsky, V.V., Ogurtsov, M.I., 2017. “Modeling of communication networks of mobile HLA distance-controlled systems”. Bulletin of the Khmelnitsky National University, 1(245), pp. 160–165. (In Ukrainian).
  8. Anureev, I.I., 1975. Reusable rockets. Moscow, Voenizdat, 214 p. (In Russian).
  9. Dynetics selected for demonstration phase of DARPA’s Gremlins program. [online] Available at: < 2018/dynetics-selected-for-demonstration-phase-of-darpas-gremlins-program> [Accessed 18 May, 2018].
  10. Mr. Scott Wierzbanowski. Gremlins. [online] Available at: <> [Accessed 30 May, 2018].
  11. The Gremlins Program Fact Sheet. [online] Available at: <> [Accessed 21 May, 2018].
  12. Collaborative Operations in Denied Environment (CODE) Phase 2 Flight Tests. [online] Available at: <> [Accessed 21 May, 2018].
  13. Samarskyi, A.A., Mikhailov, A.P., 2002. Mathematical Modeling: Ideas. Methods. Examples. Moscow, Fizmatlit, 320 p. (In Russian).
  14. Chuyev, Yu.V., 1970. Operations Research in Military Affairs. Moscow, Voenizdat, 256 p. (In Russian).
  15. Ventzel, E.S., 1964. Introduction to the study of operations. Moscow, Soviet Radio, 1964, 388 p. (In Russian).
  16. Modern problems of computational mathematics and mathematical modeling, 2005. In-t of Computation Mathematics. Moscow, Science, T.2. Mathematical modeling. 405 p. (In Russian).

Received 14.12.2018